Analysis of Variance
Department of Educational Psychology
Agenda
1 Overview and Introduction
2 Sampling, Statistics, and Parameters
3 Scales of Measurement and Describing Variables
4 Descriptive Statistics and Plots
5 Hypothesis Testing
6 Conclusion
This material is to help refresh your knowledge of foundational statistics concepts, ideas, and descriptives, prior to more advanced topics to be covered in this course; this will be especially useful if you have not recently taken a statistics class
Students will be able:
Analysis of variance, or ANOVA for short, is the core focus of this class, but is a complex technique that benefits from a good understanding of foundational statistics
Prior to us learning about ANOVA, we’ll briefly recap the things you’ve likely already learned in a previous stats class, i.e., EDPS-641
Though this is likely review, I still encourage you still engage and refresh yourself on these ideas now, so you don’t get lost later on!
Agenda
1 Overview and Introduction
2 Sampling, Statistics, and Parameters
3 Scales of Measurement and Describing Variables
4 Descriptive Statistics and Plots
5 Hypothesis Testing
6 Conclusion
Agenda
1 Overview and Introduction
2 Sampling, Statistics, and Parameters
3 Scales of Measurement and Describing Variables
4 Descriptive Statistics and Plots
5 Hypothesis Testing
6 Conclusion
Agenda
1 Overview and Introduction
2 Sampling, Statistics, and Parameters
3 Scales of Measurement and Describing Variables
4 Descriptive Statistics and Plots
5 Hypothesis Testing
6 Conclusion
| Student | Q1 | Q2 | Q3 | Q4 | Q5 |
|---|---|---|---|---|---|
| Student 1 | 1 | 0 | 1 | 1 | 0 |
| Student 2 | 0 | 1 | 0 | 1 | 1 |
| Student 3 | 1 | 1 | 1 | 0 | 0 |
| Student 4 | 0 | 0 | 1 | 0 | 1 |
| Student 5 | 1 | 1 | 0 | 1 | 1 |
\[ \bar{x} = \frac{x_1 + x_2 + x_3 + .... + x_n}{n} \]
\[ s^2 = \frac{\sum{(x-\bar{x})^2}}{n-1} \]
\[ \sigma^2 = \frac{\sum{(x-\mu)^2}}{n} \]
\[ s = \sqrt{\frac{\sum{(x-\bar{x})^2}}{n-1}} \]
\[ \sigma = \sqrt{\frac{\sum{(x-\mu)^2}}{n}} \]
The range is the difference between the largest and smallest values in the data
The interquartile range (IQR) is the 75th percentile (upper quartile, \(Q_3\)) minus the 25th percentile (lower quartile, \(Q_1\)). It is the width of the interval that contains the middle 50% of the data.
There are several characteristics that are not well described as either Measures of Dispersion or Measures of Central Tendency, but still helpful in understanding the layout of a continuous distribution
Usually, we use The Normal Distribution as an “ideal”, and describe variables’ distribution in how it relates to the normal distribution
A frequency histogram, at first glance, looks much like a bar plot, as described prior.
However, rather than use individual discrete points or labels, histograms will group values by a defined bin width, and count the frequencies of values within that bin
Simple frequency is a count of the number of cases – or frequency - that fall in the different categories or that obtain certain scores.
Relative frequency is the proportion or percentage of cases for each score in the distribution
Cumulative frequency is a count of the number of cases that fall below a certain score. A cumulative frequency is provided for all scores in the distribution
Cumulative relative frequency is the proportion or percentage of cases that fall below a certain score.
Agenda
1 Overview and Introduction
2 Sampling, Statistics, and Parameters
3 Scales of Measurement and Describing Variables
4 Descriptive Statistics and Plots
5 Hypothesis Testing
6 Conclusion
In statistics, hypothesis testing is the process by which we evaluate whether data supports making a certain conclusion beyond a reasonable doubt
We have certain steps to work through a hypothesis test:
Agenda
1 Overview and Introduction
2 Sampling, Statistics, and Parameters
3 Scales of Measurement and Describing Variables
4 Descriptive Statistics and Plots
5 Hypothesis Testing
6 Conclusion
This was a (not so) quick recap of basics ideas in describing and examining data, and the nature of variables, samples, populations, and distributions
We saw examples of how to appropriately apply certain descriptive procedures, and also discussed some of the limitations
We also began talking about the framework of hypothesis testing and how that provides a way for us to determine if results are significant or not
Module 1 Lecture - Review of Scale of Measurement, Research Design, and Descriptive Statistics || Analysis of Variance